Direct Variations Using Unitary Method: In general, the unitary method is helpful to find the value of a single unit from the given multiple. After the value of a single unit has been identified, the value of the required units may be estimated by multiplying the single value unit by the number of units required. This method is commonly used to compute ratios and proportions.
We may find the missing value by employing the unitary technique. 7th grade math students can learn the definition of the unitary method in direct variation with solved examples in this article.
What is Meant by Unitary Method using Direct Variations?
The unitary method helps to calculate the value of one unit from the value of many units and the value of many units from the value of one unit. It is a method that we employ for the vast majority of mathematical computations.
The unitary approach is used for solving problems that involves first determining the value of a single unit and then multiplying that value by the required value. This technique is used to calculate the value of a unit from the value of a multiple.
Types of Unitary Methods
The unitary approach begins with determining the value of a unit quantity in order to compute the value of the various number of units. It comes in two varieties.
- Direct variation
- Indirect variation
Direct Variation
In the direct variation, a rise in one quantity causes an increase in another; similarly, a reduction in one number causes a decrease in another. For example, when the number of products rises, so does their cost.
Furthermore, the quantity of work completed by a single person will be smaller than the amount of work completed by a group of individuals. As a result, as the number of workers increases, so will the amount of work done.
Direct variation is its inverse. The same as inversely proportional. When the value of one item rises, the value of another quantity falls. For example, increasing the pace allows us to complete the distance in less time. As a result, as speed increases, time decreases.
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Real-Time Application of Unitary Methods
The unitary technique has several real-world applications, including:
- The unitary technique is quite useful in tackling numerous challenges that we encounter in our daily lives.
- If the speed and distance are supplied in various values, calculate the speed of a vehicle over a certain distance.
- To determine the number of men needed to do a specified amount of work.
- To determine the area of a square of a certain length if the area-to-side ratio is specified.
- If the cost and number of things are supplied in various quantities, determine the cost of a specified number of objects.
- To calculate the proportion of a quantity.
Important Note:
- Multiplying the number of one quantity by the number of quantities provides the value of several quantities.
- Divide the value of several values by the number of quantities to find the value of one.
Solved Examples of Direct Variations Using Unitary Method
1. Labour is paid Rs 876 for 12 days of service. How many days need he labour in order to earn Rs 1800?
This is a direct variation scenario, as money is earned for working additional days.
A labourer earns Rs 876 in 12 days.
A labourer earns Rs 1 in 12/876 days.
A labourer earns Rs 1800 in
12/876 × 1800 days.
As a result, a labourer earns Rs 1800 in 25 days.
2. Determine how much $7 men and 13 women will make in a day if 6 men and 5 women can earn $480 per day.
This is a case of direction variation.
In a given day, more men can make more.
6 men may make $ 480 in a day.
1 man can make $480/6, while 7 men can earn $480/6, for a total of $560.
Furthermore, 5 women can make $ 480, whereas 1 woman can earn $ 480/5 = $96.
13 women can earn a total of $96 * 13 = $1248.
As a result, 7 men and 13 women can earn $(560 + 1248) = $ 1808.
3. A truck can travel 240 km on 40 litres of fuel. How much mileage will it cover in 16 litres of petrol?
This is another case of direct variation.
Less gas means less distance travelled.
Distance travelled in 40 litres of fuel Equals 240 km.
Distance travelled per litre of fuel = 240/40 km.
Distance travelled in 12 litres of fuel = 240/40 * 16 km
As a result, the distance travelled with 16 litres of fuel is 96 kilometres.
FAQ’s on Unitary Method Direct Variations
1. What is the unitary method formula?
The unitary method’s formula is to get the value of a single unit and then multiply that value by the number of units to get the required value.
2. What is the best way to solve a unitary problem?
The unitary method is a way of solving problems that involve first determining the value of one unit and then multiplying that value by the unknown value.
3. What are the unitary method’s applications?
The unitary method has numerous practical applications. It may be used to solve problems including distance, time, effort, speed, ratio, and proportion. It may be used to determine the cost of items or their price depending on local and worldwide market trends.
4. How is the unitary technique mathematically defined?
The unitary approach is a way of solving problems that involves first calculating the value of a single unit and then multiplying that value by the essential value. This approach, on the other hand, may be used to calculate the value of a unit from the value of a multiple, and hence the value of a multiple.